High stress concentration near a hydraulic fracture can generate a process or plastic zone near the fracture tip or around the opened fracture surface. The fracture geometry can be significantly different from that if such a plastic deformation is ignored. Fracture design and productivity based on a linear elastic fracture mechanics (LEFM) model can be compromised if the plastic deformation and process zone dominate the fracturing process. In addition, the stresses and deformations outside the fracture tip region may be governed by an elastoplastic behaviour which is independent of the aforementioned crack tip plasticity. A combined poro-elastoplastic fracture mechanics model is therefore proposed in this work to describe the dynamic process of fracture propagation and the stresses and deformations in the vicinity of the moving fracture and its surroundings. The stress intensity factor in the elastoplastic interface is utilized to compare a modified fracture toughness, in which the incremental fracture length is added up, with that of the process zone. Consequently, both the fracture length and width differ from those if a LEFM is used, as plastic deformation may take place both near the tip and around the two flanks of the fracture, and this may change the fracturing design and therefore the productivity evaluation significantly.


Hydraulic fracturing technology is applied to unconventional and low-permeability formations to enhance oil and gas production. During a fracturing process an opening is created and the width and length of such an opening are used to evaluate the productivity in practice. A fracture shape is normally postulated and elastic deformation is assumed. Then, the length and the width are used to define the fracture conductivity, skin, and ultimately productivity (Valco and Economides, 1995). To calculate the stresses and the deformation near the fracture or inside the formation, four computational elements may be introduced:

  1. the deformation of fracture surfaces;

  2. the fluid flow within the fracture;

  3. leak-off from the fracture surface into the formation due to poro-elastoplastic effects,

  4. the fracture propagation (Mendelsohn, 1984a, 1984b; Li et al., 2015).

Linear elasticity is commonly used as the deformation law of rock; some empirical laws are set for the fluid within the fracture; linear elasticity fracture mechanics theory is usually adopted for the dynamic propagation processes; an additional term is often given to the fluid flow equation to calculate the leak-off effects, which is normally treated by means of a coupling factor for flow between the fracture and formations adjacent to the fracture (Carter, 1957).

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